Q.Define angular dispersion for a prism. Obtain its expression for a thin prism. Relate it with the refractive indices of the material of the prism for corresponding colours.

[!TLDR] Angular dispersion delta_VR=delta_V-delta_R; for a thin prism delta=A(n-1) per colour, so delta_VR = A(n_V - n_R). [!ANSWER] delta_VR = delta_V - delta_R = A(n_V - n_R), for a thin prism of angle A.

Angular dispersion, for a prism, is defined as the ANGULAR SEPARATION between the emergent directions of two chosen colours (usually the extremes, violet and red) after passing through the prism -- i.e. the difference between their respective total deviations, delta_VR = delta_V - delta_R. For a THIN prism (refracting angle A less than about 10 degrees) at small angles of incidence, the general deviation relation collapses (via the small-angle approximation applied throughout Snell's law) to delta = A(n-1) for any single colour of refractive index n -- a deviation independent of the incidence angle. Applying this separately to violet (index n_V) and red (index n_R) and subtracting: delta_VR = delta_V - delta_R = A(n_V - 1) - A(n_R - 1) = A(n_V - n_R). This directly relates the angular dispersion to the DIFFERENCE between the two colours' refractive indices (multiplied by the prism angle A): a material whose refractive index changes more sharply between red and violet (a larger n_V - n_R) produces proportionally more angular dispersion for the same prism angle, and a larger prism angle A produces proportionally more dispersion for the same material. [!ANSWER] delta_VR = A(n_V - n_R), derived from the thin-prism deviation formula delta=A(n-1) applied separately to violet and red and subtracted.

Start from the thin-prism deviation formula delta=A(n-1), apply it separately to the two extreme colours violet and red, and subtract to define and derive the angular-dispersion expression delta_VR=A(n_V-n_R).

Quoting delta_VR as simply 'the difference in refractive index' without the prism-angle factor A, or without first establishing the thin-prism deviation formula delta=A(n-1) that the dispersion expression is built from.